Method of nano thin film thickness measurement by auger electron spectroscopy

ABSTRACT

A system and method for measuring the thickness of an ultra-thin multi-layer film on a substrate is disclosed. A physical model of an ultra-thin multilayer structure and Auger electron emission from the nano-multilayer structure is built. A mathematical model for the Auger Electron Spectroscopy (AES) measurement of the multilayer thin film thickness is derived according to the physical model. Auger electron spectroscopy (AES) is first performed on a series of calibration samples. The results are entered into the mathematical model to determine the parameters in the mathematical equation. The parameters may be calibrated by the correlation measurements of the alternate techniques. AES analysis is performed on the ultra-thin multi-layer film structure. The results are entered into the mathematical model and the thickness is calculated.

BACKGROUND INFORMATION

The present invention relates to thin-films on substrates. Specifically,the present invention relates to the use of Auger Electron Spectroscopyin the measurement of the thickness of an ultra-thin film on asubstrate.

Ultra-thin films with thickness of less than five nanometers have foundincreasing application in the development of nano-technology. The exactthickness of such ultra-thin film is important for both the basicstudies of multi-layer nano-structures and in the technicalspecifications of nano-device fabrication. For example, in theproduction of a magnetic head for a hard disc drive (HDD); an ultra-thindiamond-like-carbon (DLC) film is coated on the slider substrate, withan ultra-thin silicon (Si) film as the transition layer in between, toprotect the writer/reader sensor. With the rapid increase of the HDDrecording density to 80 G bits/inch², the flying height of the sliderover the disc has been reduced to about 10 nm. Correspondingly, thethickness of DLC and Si layer must be reduced to 1.5 to 2.5 nm, and theaccurate measurement of the ultra-thin film thickness becomes a keyfactor in the advanced giant magnetic resistance (GMR) head research andmanufacturing. Several nano-metrology techniques, which can meet theabove demand to some extent, exist in the prior art.

As shown in FIG. 1 a, an Atomic Force Microscope (AFM) may test thethickness of an ultra-thin film 102 coated on a substrate 104 byscanning with an AFM tip 106 the depth of a photoresist-created groove108 on the film 102. AFM has a resolution of 10 nm on the X-axis andY-axis and a resolution of 0.1 nm on the Z-axis. The disadvantage of AFMis that it requires elaborate sample preparation and can only measurethe thickness of a mono-layer or the combined total thickness of amulti-layer film. Therefore, the usefulness of AFM is limited tocalibration applications.

As shown in FIG. 1 b, a Transmission Electron Microscope (TEM) is asuperior technique to measure an ultra-thin diamond-like carbon (DLC)layer thickness. A TEM is powerful in nano-scale dimension measurement,being able to directly observe and measure the ultra-thin film thicknessat the one-millionth resolution, or even higher magnification withspatial resolution of about 0.1 nm. However, this method requirescomplicated and time-consuming sample preparation by a Focus Ion Beam(FIB), to create a cross section and, then, measuring the thickness byTEM. Such a “destructive” measurement is undesirable in many cases andnot suitable for routing quality monitoring of a nano-device production.

Electron Spectroscopy for Chemical Analysis (ESCA) is a third knownmethod for nano-thin film thickness measurement. ESCA is anon-destructive method used to measure the diamond-like carbon thicknesson a silicon chip with an area resolution of approximately 1 mm, and insome cases up to 10 μm. As shown in FIG. 1 c, the sample has a substrate110 composed of Al₂O₃TiC and is covered with a silicon layer 112 and aDLC layer 114. In this ESCA method, incident X-ray photon 116 causes thephotoelectron emission at a specific angle (O) from the surface of theDLC layer 114. Using the concentrations of silicon (Si %), aluminum (Al%), and carbon (C %) in the sample, calculated from the ESCA measuredSi, AL, and C photoelectron signal intensities, the thickness of the DLClayer d 114 can be determined with the following equations:d = λ  sin   θ ⋅ ln (1 + aR)${a = {A \cdot \frac{{BR}^{\prime}}{1 + {BR}^{\prime}}}},{R^{\prime} = \frac{{Si}\%}{{Al}\%}},{R = \frac{{C\%} - {J*{Si}\%}}{{Si}\%}}$${A = \frac{I_{Si}^{\infty}}{I_{C}^{\infty}}},{B = \frac{I_{Al}^{\infty}}{I_{Si}^{\infty}}}$The variable a represents the intensity factor, the variables R and R′represent modification factors, the variable λ represents theattenuation length of a Si photoelectron passing by carbon layers, and Jrepresents the ratio of SiC in Si layer. Using the same inputs, thethickness of the silicon layer d′ 112 can be determined using thefollowing equations: d^(′) = λ^(′)sin   θ ⋅ ln (1 + Br)$r = \frac{{Si}\%}{{Al}\%}$The variable r represents modification factors and the variable λ′represents the attenuation length of the A1 photoelectron passing by thesilicon layer. However, the area resolution of the ESCA method isnormally in the millimeter range and about 10 μm at best. Therefore,this technique is not applicable to the thickness measurements of smallarea, such as down to the sub-micrometer, or even nanometer size, thatis absolutely important for a submicro-device or nano-device researchand manufacturing.

An Auger Electron Spectroscopy (AES) depth-profile method can be used tomeasure the relative thickness of an ultra-thin film. AES is an advancedsolid surface analysis technique, based on the “Auger Effect”. The Augerprocess is initiated with the removal of a core electron by an energeticprimary electron beam, creating an ion with an inner shell vacancy. Inthe relaxation of the exited ion, an electron from a higher energy levelfills the inner shell vacancy with the simultaneous emission of anotherhigher level electron, called an “Auger Electron”. The kinetic energy ofthe Auger electron is determined by the energy difference of the related3 levels and is characteristic for the atom in which the Auger processoccurs. An Auger electron spectrum plots the number of electronsdetected as a function of electron kinetic energy. Elements areidentified by the energy positions of the Auger peaks, while theconcentration of an element is related to its Auger signal intensity.Furthermore, both theoretical and experimental research have shown thatthe mean free path of an Auger electron emission is less than 5 nm,meaning only a few to a dozen atomic layers can be detected by AES. AESis thus applied for the elementary composition analysis of a solidsurface. AES and an Argon ion beam etching of the surface may becombined to perform a compositional depth profile analysis. Therefore,the thickness of a thin film can be obtained by taking account of theArgon ion sputtering time to remove the thin film layer, with thecalibrated sputtering rate in hand. This method is also a destructivemethod and the accurate stuttering rate for a certain material is oftendifficult to obtain.

Lastly, an AES physical-mathematical model, for measuring the thicknessof Cobalt thin film on a Nickel-Iron alloy substrate, has been reported.An example, as shown in FIG. 1 d, includes a substrate 118 with a thinfilm 120 layer applied. The substrate may be a nickel-iron alloy, withthe thin film layer 120 made of cobalt. The angle 122 of an emissionAuger electron 124 from normal is 43°. An AES physical-mathematics modelmethod may be used to determine the thickness 126 of the thin film layer120. The mathematics model is as follows:$t = {\lambda_{Ni}^{Co}\cos\quad\theta\quad\ln\quad\left( {\frac{I_{Co}}{a*I_{NiFe}} + 1} \right)}$a = I_(Co)^(∞)/I_(NiFe)^(∞)The variable λ_(Ni) ^(Co) represents the attenuation length of Augerelectron of Ni element in substrate layer 118 through Co layer 120. Thismethod applies only to a monolayer Cobalt film on a nickel-iron alloysubstrate.

What is needed is a way to measure ultra-thin film (≦5 nm) layers ofeither single or double layers in an area of about 100 nm². For example,in the manufacturing of magnetic recording head, a key component devicefor computer Hard Disk Drive (HDD), the slider surface is coated with anultra-thin film of diamond like carbon (DLC), with Si as the transitionlayer between DLC and AL₂O₃—TiC substrate. The flying height of a sliderover a disk is currently down to about 10 nm. To control the thicknessof the DLC and Si layer to between 2.5 nm and 1.5 nm becomes essentialfor the magnetic head production. Meanwhile, the key components of theslider, the writer and reader sensor are of a submicrometer or nanometersize, making the nano-metrology of the precise thickness measurement ofthe double layer ultra-thin film is vitally important for high-techproduction. In addition, the measurement is supposed to be done withoutthe need for a complicated sample preparation, or non-destructive andefficient enough to satisfy industrial testing.

BRIEF DESCRIPTION OF THE DRAWINGS

FIGS. 1 a-d illustrate various methods for measuring thin film layers asknown in the art.

FIG. 2 illustrates the physical model according to the presentinvention.

FIG. 3 illustrates one embodiment of an AES apparatus according to thepresent invention.

FIG. 4 illustrates in a flowchart one embodiment of a method formeasuring thin film layers.

FIG. 5 illustrates in a block diagram the positioning of four differentareas of measurement.

DETAILED DESCRIPTION

A system and method for measuring the thickness of an ultra-thinmulti-layer film structure on a substrate is disclosed. A physical modelof an Auger emission from a nano multilayer structure is built. Amathematical model of Auger electron spectroscopy (AES) measurement ofultra-thin film thickness is derived according to the physical model. Byperforming the AES measurements on a series of calibration samples, theparameters in the mathematical model are determined. The parameters maybe calibrated by comparing the results to the results from correlationmeasurement by alternative techniques, such as transmission electronmicroscope (TEM), atomic force microscope (AFM), and electronspectroscopy for chemical analysis (ESCA), establishing a physicalmodel. AES analysis is performed on the practical samples to measure thesignal intensity of the related elements in the ultra-thin multi-layerfilm structure. The results are input into the mathematical model andthe thickness is calculated.

FIG. 2 illustrates in a schematic diagram one embodiment of a physicalmodel as practiced in the present invention. A physical model 210 of asubstrate (Z) 220 with double-layer ultra-thin film is created. In oneembodiment, the ultra-thin film layer has a first layer 230, or X layer,and a second layer 240, or Y layer. In one embodiment, the first layer230 is a diamond like carbon (DLC) layer and the second layer 240 is asilicon layer placed on conductive ceramic layer made of Al₂O₃TiC actingas a substrate 220.

FIG. 3 illustrates in a block diagram one embodiment of an AES apparatusaccording to the present invention. The substrates 302 are loaded into asampling holder, which allows multiple substrates to be tested in rapidsuccession. A field emission primary electron gun 304 fires an electronbeam with a beam energy of between 1 and 20 keV and a beam size finelyfocused to about 10 nm, which guarantees the ultra-high spatialresolution for the sub-micro to nano-scale surface analysis. Augerelectron is ejected from the surface of the multi-layer substrates bythe incident primary electron and, then, guided into and energy analyzedby an electron energy analyzer, such as a cylinder mirror analyzer (CMA)306. The Auger electron passes through the CMA 306 and is collected atan Auger electron multi-channel detector 308. The electron detector 308will amplify the signal from the electron multiplier before forwardingit to an online computer. The online computer acts as a x-y recorder oroscilloscope to measure the signal intensities in order to perform amulti-layer ultra-thin film thickness calculation, with a mathematicalmodel derived from the physical model. In one embodiment, the tests arefirst performed on a series of calibration samples, prepared accordingto the physical model of the multilayer, ultra-thin film structure, todetermine the parameters in the mathematical model.

In a further embodiment, the parameters are calibrated by comparing theresults to the results obtained by using an atomic force microscope(AFM), a transmission electron microscope (TEM), and/or electronspectroscopy for chemical analysis (ESCA). Table I shows an example ofthe resulting comparisons. TABLE 1 The parameters calibrated by AFM andESCA data Intensity Lead Ratio ABS (Al2) Ni—Fe (Ni1) Ni—Fe—Co (Co1)(Au3) a′  0.946 2.319 2.043 5.529 a″ 1.090 1.011 1.011 1.011

Modification Lead Factor ABS (Al2) Ni—Fe (Ni1) Ni—Fe—Co (Co1) (Au3) R 1.000 1.420 1.420 1.652 R′ 1.000 1.263 1.263 0.937

Mean Free Ni—Fe Ni—Fe—Co Path ABS (Al2) (Ni1) (Co1) Lead (Au3) λ_(Si)^(DLC) 3.100 nm  3.1 nm  3.1 nm  3.1 nm λ_(Substrate) ^(Si) 2.400 nm1.951 nm 1.951 nm 1.260 nm

After the parameters have been determined, they and the mathematicalmodel are inputted into the software installed into the online computer322 of the AES. The ultra-thin film thickness can be calculated by theexperimentally obtained Auger signal intensity of substrate, the firstand the second layer material, respectively.

According to the physical model shown in FIG. 2, the mathematical modelof the AES measurement of a double-layer thin film on a substrate may bederived in the following method:${{For}\quad{the}\quad{homogeneous}},\quad{I_{A} = {\int_{1}^{\infty}{g_{A}C_{A}{\mathbb{e}}^{- \frac{x}{\lambda_{A}\cos\quad\theta}}\quad{\partial x}}}},{g_{A} = {{T(E)}{D(E)}I_{o}\sigma_{A}{\gamma_{A}\left( {1 + r_{M}} \right)}}}$

I_(A)^(∞) = g_(A)C_(A)λ_(A)^(A)cos   θ

${{For}\quad{the}\quad Z\quad{substrate}},{I_{X}^{X} = {g_{X}C_{X}{\int_{0}^{1}{{\mathbb{e}}^{- \frac{x}{\lambda_{X}^{X}\cos\quad\theta}}\quad{\partial x}}}}},{I_{Y}^{X} = {g_{Y}C_{Y}{\int_{1}^{d}{{{\mathbb{e}}^{- \frac{({x - t})}{\lambda_{Y}^{Y}\cos\quad\theta}} \cdot {\mathbb{e}}^{- \frac{t}{\lambda_{Y}^{X}\cos\quad\theta}}}{\partial x}}}}},{I_{Z}^{X} = {g_{Z}C_{Z}{\int_{d}^{\infty}{{{\mathbb{e}}^{- \frac{t}{\lambda_{Z}^{X}\cos\quad\theta}} \cdot {\mathbb{e}}^{- \frac{({d - t})}{\lambda_{Z}^{Y}\cos\quad\theta}} \cdot {\mathbb{e}}^{- \frac{({x - d})}{\lambda_{Z}^{Z}\cos\quad\theta}}}{\partial x}}}}}$

${I_{X}^{X} = {I_{X}^{\infty} \cdot \left( {1 - {\mathbb{e}}^{- \frac{t}{\lambda_{X}^{X}\cos\quad\theta}}} \right)}},{I_{Y}^{Z} = {I_{Y}^{\infty} \cdot {{\mathbb{e}}^{- \frac{t}{\lambda_{Y}^{X}\cos\quad\theta}}\left\lbrack {1 - {\mathbb{e}}^{- \frac{({d - t})}{\lambda_{Y}^{Y}\cos\quad\theta}}} \right\rbrack}}},{I_{Z}^{X} \approx {I_{Z}^{\infty} \cdot {\mathbb{e}}^{- \frac{t}{\lambda_{Z}^{X}\cos\quad\theta}} \cdot {\mathbb{e}}^{- \frac{({d - t})}{\lambda_{Z}^{Y}\cos\quad\theta}}}}$

λ_(X)^(X) = λ_(Y)^(X), λ_(X)^(Y) = λ_(Y)^(Y)${I_{X}^{X} = {I_{X}^{\infty} \cdot \left( {1 - {\mathbb{e}}^{- \frac{t}{\lambda_{Y}^{X}\cos\quad\theta}}} \right)}},{I_{Y}^{X} = {I_{Y}^{\infty} \cdot {{\mathbb{e}}^{- \frac{t}{\lambda_{Y}^{X}\cos\quad\theta}}\left( {1 - {\mathbb{e}}^{- \frac{({d - t})}{\lambda_{Z}^{Y}\cos\quad\theta}}} \right)}}},{I_{Z}^{X} = {I_{Z}^{\infty} \cdot {\mathbb{e}}^{- \frac{({d - t})}{\lambda_{Z}^{Y}\cos\quad\theta}} \cdot {\mathbb{e}}^{- \frac{t}{\lambda_{Z}^{X}\cos\quad\theta}}}}$

${{By}\quad\frac{I_{Y}^{X}}{I_{Z}^{X}}},{{{If}\quad a^{\prime}} = \frac{I_{Z}^{\infty}}{I_{Y}^{\infty}}},{R^{\prime} = \frac{I_{Y}^{X}}{I_{Y}^{\infty}}},{{{then}\quad\left( {d - t} \right)} = {\lambda_{Z}^{Y}\cos\quad\theta\quad{\ln\left( {{a^{\prime} \cdot R^{\prime}} + 1} \right)}}}$${{By}\quad\frac{I_{X}^{X}}{I_{Y}^{X}}},{{{If}\quad a} = {\frac{I_{Y}^{\infty}}{I_{X}^{\infty}} \cdot \left( {1 - {\mathbb{e}}^{- \frac{({d - t})}{\lambda_{Z}^{Y}\cos\quad\theta}}} \right)}},{R = \frac{I_{X}^{X}}{I_{Y}^{X}}},{{{then}\quad t} = {\lambda_{Y}^{X}\cos\quad{\theta \cdot {\ln\left( {{a \cdot R} + 1} \right)}}}}$${{{If}\quad a^{''}} = \frac{I_{Y}^{\infty}}{I_{Y}^{\infty}}},{{{then}\quad a} = {a^{''} \cdot \frac{a^{\prime}R^{\prime}}{1 + {a^{\prime}R^{\prime}}}}}$In the above derivation, the variable “C_(A)” represents concentrationof element A. The variable “λ_(A)” represents the attenuation length ofAuger electron. The variable “θ” represents emission angle between thesurface normal and the detector direction. The variable “σ_(A)”represents a cross section of Auger process. The variable “T(E)”represents transmission factor, a function of kinetic energy E of theAuger electron. The variable “D(E)” represents the detection efficiencyof the electron multiplier, a factor that may vary with time. Thevariable “r_(M)” represents an electron backscatter factor that ismatrix dependent. The variable “I_(o)” represents the primary current.

FIG. 4 illustrates in a flowchart one embodiment of a method fordetermining ultra-thin film thickness according to the presentinvention. The process starts (Block 405) by designing a physical modelof the ultra-thin, multi-layer film structure (Block 410). Then, amathematical model for calculating the thickness of the ultra-thin,multi-layer film structure is derived based on the structure of thephysical model (Block 415). If the thickness (d) of the ultra-thin,multi-layer film structure is greater than 5 nanometers (Block 420), thethickness (t) of the first layer is modeled using the following equation(Block 425):t=λ _(Y) ^(X) cos θ·In(a·R+1).If the thickness (d) of the ultra-thin, multi-layer film structure isless than or equal to 5 nanometers (Block 420), the thickness (t) of thefirst layer is modeled using the following equation:t=λ _(Y) ^(X) cos θ·In(a·R+1)and the thickness (d−t) of the second layer is modeled using thefollowing equation (Block 430):(d−t)=λ_(Z) ^(Y) cos θIn(a′·R′+1).An AES measurement is performed on a series of calibration samples tomeasure the signal intensities of the related elements in a multilayerstructure of known-thickness (Block 435). Then, the acquired data isinput into the mathematical model to determine all the parameters in themathematical equation (Block 440). The parameters are calibrated bycomparing the calculated thickness with the results provided by TEM,AFM, and ESCA (Block 445). Once all the proper parameters are determinedand calibrated, the physical-mathematical model may be consideredestablished. An AES measurement may then be performed on the practicalsamples of the ultra-thin film structure (Block 450). The thickness iscalculated using the mathematical model (Block 455), finishing theprocess (Block 460).

This measurement technique may be applied in the data storage industry,such as in the mass production of hard disk drives (HDD), GMR headmanufacturing, head quality routine monitoring, failure analysis,research and development, and others.

In one embodiment, the nano metrology method is applied in themeasurement of the thickness of ultra-thin DLC and Si coating layers onthe GMR head of the HDD. FIG. 5 illustrates in a block diagram thepositioning of four different areas of measurement. Mass producedrowbars 510, usually sized at 1×40 mm, are cut from the magneticrecording wafer and coated with ultra-thin DLC. Silicon acts as thetransition layer between DLC and the substrate material, Al₂O₃—TiC, toprotect the pole area (writer/reader sensor). Then, the air-bearingsurface (ABS) 520 is created by photolithography on each slider (1×1mm). AES, ESCA, AFM and TEM are applied to measure the DLC and Sithickness. The target thickness of the DLC/Si layers are ranged from 1.5nm to 4.0 nm, respectively. The results of DLC and Si thicknessmeasurements on the substrate of Al₂O₃TiC (rowbar, sized in 1×40 mm) andABS of slider (0.2-0.5 mm), a Ni—Fe alloy 530 (shield of writer andreader sensor, 1-5 μm), and on a substrate of Au/Cu 540 (lead material,40 nm) are listed in the table 2. TABLE 2 The comparison of AES, ESCA,AFM and TEM data Measured Area Rowbar ABS on (without ABS) Slider/RowbarShield Lead method DLC Si Total DLC Si Total DLC Si Total DLC Si TotalTarget (Å) 25 10 35 25 10 35 25 10 35 25 10 35 AES data (Å) 24.7 30.655.3 24.7 30.6 55.3 29.8 30 59.8 28.6 32.7 61.3 ESCA data (Å) 29.2 25.754.9 — — — — — — — — — AFM data (Å) — — 57.9 — — 57.9 — — 57.9 — — 57.9TEM data (Å) — — 60 — — 60 — — 60 — — 60 Target (Å) 10 25 35 10 25 35 1025 35 10 25 35 AES data (Å) 15 35.6 50.6 15 35.6 50.6 12.6 40.8 53.414.8 40.4 53.2 ESCA data (Å) 11.9 37.2 49.1 — — — — — — — — — AFM data(Å) — — 50.5 — — 50.5 — — 50.5 — — 50.5 TEM data (Å) — — 48 — — 48 — —48 — — 48 Target (Å) 40 25 65 40 25 65 40 25 65 40 25 65 AES data (Å)48.9 — — 48.9 — — 47.4 — — 44.6 — — ESCA data (Å) 37.3 44.2 81.5 — — — —— — — — — AFM data (Å) — — 82.2 — — 82.2 — — 82.2 — — 82.2 TEM data (Å)— — 78 — — 78 — — 78 — — 78 Target (Å) 25 40 65 25 40 65 25 40 65 25 4065 AES data (Å) 49.5 — — 49.5 — — 47.5 — — 50 — — ESCA data (Å) 28.250.8 79 — — — — — — — — — AFM data (Å) — — 83.7 — — 83.7 — — 83.7 — —83.7 TEM data (Å) — — 84 — — 84 — — 84 ——— — 84TEM and AFM are applied as the calibration measurement as they needcomplicated sample preparation and are the destructive methods. AES andESCA are the non-destructive methods and do not need complicated samplepreparation. However, due to the poor spatial resolution, ESCA can onlymeasure the DLC/Si thickness on the rowbar without ABS. In contrary, AESis the only method, which has the all advantages of non-destructive,non-complicated sample preparation, efficient and can measure all thearea, including rowbar, ABS of slider, pole area, and even the nano areaof the GMR sensor and the lead.

1. A thickness measurement method, comprising: performing an Augerelectron spectroscopy analysis on a thin film layer on a substrate;collecting a set of auger electron spectroscopy data of the thin filmlayer; performing a calculation on the set of data using a predeterminedmathematical model; and determining a thickness of the thin film layerbased on the calculation.
 2. The thickness measurement method of claim1, wherein at least a first thin film layer and a second thin film layerhaving a combined thickness are applied to the substrate.
 3. Thethickness measurement method of claim 2, wherein both thin film layersare ultra-thin film layers of less than or equal to 5 nanometerscombined.
 4. The thickness measurement method of claim 3, furthercomprising: determining a thickness of the first film layer (t) by usingan attenuation length between the first thin-film layer (X) and thesecond thin-film layer (Y) (λ), an Auger electron path angle from normal(θ), a first intensity ratio (a) and a first modification factor (R), ina mathematical model as follows:t=λ _(Y) ^(X) cos θ·In(a·R+1); and determining a thickness of the firstfilm layer (d−t) by using an attenuation length between the secondthin-film layer (X) and the substrate (Y) (λ), an Auger electron pathangle from normal (θ), a second intensity ratio (a′) and a secondmodification factor (R′), in a mathematical model as follows:(d−t)=λ_(Z) ^(Y) cos θIn(a′·R′+1).
 5. The thickness measurement methodof claim 2, further comprising determining a thickness of the first filmlayer (t) by using an attenuation length between the first thin-filmlayer (X) and the second thin-film layer (Y) (λ), an Auger electron pathangle from normal (θ), an intensity ratio (a″) and a modification factor(R), in a mathematical model as follows:t=λ _(Y) ^(X) cos θIn(1+a″·R).
 6. The thickness measuring method ofclaim 1, further comprising: building a physical model of the thin filmlayer on the substrate; deriving a mathematical model of Auger electronemission from the thin film layer on the substrate; determining valuesfor a set of parameters for the mathematical model using Auger electronspectroscopy; and calibrating the set of parameters by correlationmeasurements using alternate techniques.
 7. The thickness measurementmethod of claim 6, wherein the alternate measurement techniques are froma group consisting of an atomic force microscope, a transmissionelectron microscope, and electron spectroscopy for chemical analysis. 8.The thickness measurement method of claim 6, further comprising alteringthe predetermined mathematical model for different physical models.
 9. Aset of instructions residing in a storage medium, said set ofinstructions capable of being executed by a processor to implement amethod for processing data, the method comprising: performing an Augerelectron spectroscopy on a thin film layer on a substrate; collecting aset of data from the auger electron spectroscopy of the thin film layer;performing a calculation on the set of data using a predeterminedmathematical model; and determining a thickness of the thin film layerbased on the calculation.
 10. The set of instructions of claim 9,wherein at least a first thin film layer and a second thin film layerhaving a combined thickness are applied to the substrate.
 11. The set ofinstructions of claim 10, wherein both thin film layers are ultra-thinfilm layers of less than or equal to 5 nanometers combined.
 12. The setof instructions of claim 11, further comprising: determining a thicknessof the first film layer (t) by using an attenuation length between thefirst thin-film layer (X) and the second thin-film layer (Y) (λ), anAuger electron path angle from normal (θ), a first intensity ratio (a)and a first modification factor (R), in a mathematical model as follows:t=λ _(Y) ^(X) cos θ·In(a·R+1); and determining a thickness of the firstfilm layer (d−t) by using an attenuation length between the secondthin-film layer (X) and the substrate (Y) (λ), an Auger electron pathangle from normal (θ), a second intensity ratio (a′) and a secondmodification factor (R′), in a mathematical model as follows:(d−t)=λ_(Z) ^(Y) cos θIn(a′·R′+1).
 13. The set of instructions of claim10, further comprising determining a thickness of the first film layer(t) by using an attenuation length between the first thin-film layer (X)and the second thin-film layer (Y) (λ), an Auger electron path anglefrom normal (θ), an intensity ratio (a″) and a modification factor (R),in a mathematical model as follows:t=λ _(Y) ^(X) cos θIn(1+a″·R).
 14. The set of instructions of claim 9,further comprising: determining values for a set of parameters for thepredetermined mathematical model using Auger electron spectroscopy on aphysical model of the thin film layer on the substrate; and calibratingthe set of parameters using alternate measurement techniques.
 15. Theset of instructions of claim 14, wherein the alternate measurementtechniques are from a group consisting of an atomic force microscope, atransmission electron microscope, and electron spectroscopy for chemicalanalysis.
 16. The set of instructions of claim 14, further comprisingaltering the predetermined mathematical model for different physicalmodels.
 17. A testing system, comprising: an Auger electron spectroscopydevice to perform an analysis on a first thin film layer and a secondthin film layer on a substrate; and a computer to collect a set of datafrom the auger electron spectroscopy of the thin film layer and toperform a calculation on the set of data using a predeterminedmathematical model to determine a thickness of the thin film layer basedon the calculation.
 18. The thickness measuring system of claim 17,wherein both thin film layers are ultra-thin film layers of less than orequal to 5 nanometers combined.
 19. The thickness measuring system ofclaim 18, wherein the computer determines a thickness of the first filmlayer (t) by using an attenuation length between the first thin-filmlayer (X) and the second thin-film layer (Y) (λ), an Auger electron pathangle from normal (θ), a first intensity ratio (a) and a firstmodification factor (R), in a mathematical model as follows:t=λ _(Y) ^(X) cos θ·In(a·R+1); and determines a thickness of the firstfilm layer (d−t) by using an attenuation length between the secondthin-film layer (X) and the substrate (Y) (λ), an Auger electron pathangle from normal (θ), a second intensity ratio (a′) and a secondmodification factor (R′), in a mathematical model as follows:(d−t)=λ_(Z) ^(Y) cos θIn(a′·R′+1).
 20. The thickness measuring system ofclaim 18, further comprising determining a thickness of the first filmlayer (t) by using an attenuation length between the first thin-filmlayer (X) and the second thin-film layer (Y) (λ), an Auger electron pathangle from normal (θ), an intensity ratio (a″) and a modification factor(R), in a mathematical model as follows:t=λ _(Y) ^(X) cos θIn(1+a″·R).